Zios and Zepts

You could begin by introducing a simpler version of the problem, for example if I can see three heads and eight legs, how many sheep and how many chickens are there in the field? Ask them to work in pairs, perhaps on mini-whiteboards, to think about this first challenge. As they work, observe different ways of recording and thinking about the problem which you can share with the whole group.

After this learners could work in pairs on the actual problem which you could present orally with the image. Headless matches and/or counters should be available for those who wish to work with something concrete. Again, listening to learners as they work can be an interesting insight to their thinking.

At the end of the session learners could share not only their solutions but also their methods. Some may have used a trial and improvement approach, either with the materials provided or using pictures; some may have written lists of multiples of $3$ and $7$ in a very systematic way and then made totals. Children could consider whether some strategies were more effective than others, although of course a strategy that is effective for one child may be very confusing for another. Having the freedom to approach this problem in any way is key here, but in talking to others, some pupils might change the way they work, which is interesting in itself.

What have you tried so far?

What happens if you replace this seven-legged creature with some three-legged creatures?

What happens if you replace these three-legged creature with some seven-legged creatures?